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What value of x is in the solution set of 9(2x + 1) < 9x – 18?

A: -4
B: -3
C: -2
D: -1

Respuesta :

carlosego

For this case we have the following inequality:

[tex] 9 (2x + 1) <9x - 18
[/tex]

Solving the inequality we have:

Distributive property:

[tex] 18x + 9 <9x - 18
[/tex]

Combine similar terms:

[tex] 18x - 9x <-9 - 18 [/tex]

[tex] 9x <- 27
[/tex]

From here, we clear the value of x:

[tex] x <-\frac{27}{3}

[/tex]

[tex] x <-3
[/tex]

Therefore, the solution is given by:

(-∞, -3)

The point that belongs to the solution is:

[tex] x = -4
[/tex]

Answer:

The value of x is in the solution set is:

A: -4

Answer:

Option A is correct

-4

Step-by-step explanation:

Given the equation:

[tex]9(2x+1)<9x-18[/tex]

Using distributive property: [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]

then;

[tex]18x+9<9x-18[/tex]

Subtract 9x from both sides we have;

[tex]9x+9<-18[/tex]

Subtract 9 from both sides we have;

[tex]9x<-27[/tex]

Divide both sides by 9 we have;

[tex]x < -3[/tex]

We can write this as:

x∈[tex](-\infty, -3)[/tex]

From the given option, only x = -4 belong to the set of the solution.

Therefore, the value of x is in the solution set of 9(2x + 1) < 9x – 18 is, -4

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